This invention relates to a control apparatus for controlling a rotor supported by a magnetic bearing to be stable up to high speed rotation, and particularly to a magnetic bearing control method and apparatus suitable for use in processing the amount of feedback in a frequency region in order that the rotor can be controlled to undergo a damping effect up to a high speed region.
In the magnetic bearing, it is difficult to make the axis of inertia of the rotor completely coincident with a predetermined axis set in the bearing. In general, the rotor has a natural frequency dependent on the shape and material of the rotor. Thus, upon rotation the rotor has a dangerous speed at which the vibration of the shaft increases. If the bearing has no damping effect, the vibration increases at the dangerous speed, so that the rotor cannot rotate. So far, in order to prevent this shaft vibration, a control apparatus has been used which detects the positional deviation of the rotating shaft from a predetermined axis, and controls the current in the electromagnetic coil for the magnetic bearing so that this deviation is suppressed, or that the damping effect can be brought about. Since the vibration of the rotor shaft has great energy in the frequency components synchronized with the rotation frequency of the rotor, the control system should greatly suppress only the vibration at such frequencies. Therefore, the control apparatus disclosed in Japanese Patent Laid-open Gazette No. 52-93853 includes a filter of analog circuits for tuning to the frequency equal to the rotation speed of the rotor so that the phase-controlled signal is supplied to the servo circuit, making great damping to the vibration frequencies. Thus, a complicated circuit is used which is formed of a differentiator, an integrator, an adder and so on.
The value of the detected deviation of the rotating shaft is subjected to Fourier transform in real time, to a signal processing in a vibration control law which is a frequency region and to reverse Fourier transform so as to produce a control signal. This control signal is used to control the current in the electromagnetic coil. Thus, an arbitrary control characteristic can be achieved with ease and satisfaction. The frequency analyzer(hereinafter, abbreviated "FFT analyzer") using the principle of discrete Fourier transform (hereinafter, abbreviated "DFT") will be described briefly with reference to FIGS. 1 and 2.
As shown in FIG. 1, an input waveform x(t) is sampled at each specified sampling period .DELTA.t, and N samples are sequentially stored in a memory (N=8). This storing process is shown at step 401 of the flowchart shown in FIG. 2. The stored values are, as illustrated, x0, x1, . . . x7. At step 402, complex amplitude values Ak, k=0-7 are found from the formula of DFT given by ##EQU1##
In this equation, j is the imaginary unit, and the following equation is given. ##EQU2## The complex amplitude values A.sub.k at each frequency .omega..sub.k show that the larger the values, the greater the vibration at the frequency. At step 403, the absolute value of the calculated result A.sub.k (k=0-7) is displayed as a bar graph.
The FFT analyzer fast executes a sequence of operations of data storing.fwdarw.DFT processing.fwdarw.displaying indicated at steps 401 to 403 in FIG. 2. The timing of this sequence of operations is shown in FIG. 1. N (N=8) samples are stored at each sampling period T=(N-1).DELTA.t of the input vibration waveform, and then the calculation of DFT and displaying are performed. During the calculation and displaying the data is stopped from being stored. Therefore, DFT calculation is not made over all the interval of the input waveform, and thus a certain interval of the vibration waveform is inevitably overlooked. This DFT calculation is based on the fact that the values of stored data x.sub.1 .about.x.sub.7 are a periodical function which is periodically repeated even out of the sampling period T. Therefore, in practice the input waveform is normally multiplied by the window function for picking up the waveform only during the sampling interval before the sampling operation.
The algorithm for the complex amplitude values. Ak of the equation (1) is a very-high speed one called the butterfly computation. As described above, the actual Fourier transform device is constructed to have various functions for its purpose. A conventional example thereof is disclosed in, for example, Japanese Patent Laid-open Gazette No. 61-196370.
The main object of the above common FFT analyzer is to display and monitor the result of having analyzed the frequencies of the vibration waveform even during the data reading stop period. The FFT analyzer is widely used because very useful information for analyzing the source of an abnormal vibration can be obtained by monitoring the complex amplitude values of the frequency components displayed as the output so as to detect the abnormal vibration. However, when it is used as the controller, the presence of the pause period prevents sufficient control. The formula of calculation for the DFT processing and finding the complex amplitude at each operation of reading the waveform data without pause period is described in, for example, "HOW TO USE FFT" written by Ankyo Intake and Masayuki Nakashima, pp.132 to 133 in Electronics science series 91 published by Sanpo shuppan, February, 1982. That is, as shown in FIG. 3, the sample values x.sub.1 to x.sub.7 at time points 0 to 7 (N=7) on the input waveform x(t) are read and stored in a memory and the complex amplitude values A.sub.k, k=0 to 7 are calculated. Then, when the value x8 at time point 8 on the input waveform x(t) is sampled, the oldest data x.sub.out x.sub.0 is discarded, the stored samples of data each are shifted left within the memory, and the read sample x.sub.in =x.sub.8 is stored in the rightmost vacancy of the memory. The complex amplitude A.sub.k at this time is given by EQU A.sub.k1 =(A.sub.ko +(x.sub.in -x.sub.out)/N.sup.-1/2)exp(j.omega..sub.k), K=0-7 (3)
This equation can be easily derived. According to the equation (3), if the complex amplitude values A.sub.k0, k=0 to 7 previously sampled are held, these complex amplitude values A.sub.k1, k=0 to 7 can be obtained by making once each of the addition, subtraction, multiplication and division of complex numbers for each k. This equation, as compared with the equation (1), is executed in much less time in real time with ease.
According to the DFT algorithm in the FFT analyzer, if the regions other than the sampling interval of the input waveform are a periodical function and coincide in its period with the sampling period of the input waveform as shown in FIG. 4A, the input waveform is subjected to Fourier transform, and the obtained complex amplitude values are shifted in phase ahead by with 90 degrees, and subjected to reverse Fourier transform so as to be a real-time waveform. Thus, at this time the waveform (which occurs during the sampling pause period) with 90 degrees ahead of the input waveform can be known. However, when as shown in FIG. 4B the period of the periodical function does not coincide with the sampling period, the above waveform cannot be obtained. In addition, if the input wave is shifted from the periodical function, correct processing cannot be performed. The control apparatus for the magnetic bearing using the DFT algorithm without the pause period is also not realized yet.